A rearrangement invariant space isometric to L_p coincides with L_p

1995/09/10 by Y. A. Abramovich, Yuri A. Abramovich, Mikhail Zaidenberg +2
Mathematics · #46E30 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA #msc:46E30

paper · pdf · doi:10.48550/arxiv.math/9509213

arxiv created 1995/09/10 · openalex publication_date 1995/09/10 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The following theorem is the main result of this note. Theorem 1. Let (E, ‖⋅‖_E) be a rearrangement invariant Banach function space on the interval [0, 1]. If E is isometric to Ł_p [0, 1] for some 1≤ p<∞, then E coincides with Ł_p [0, 1] and furthermore ‖⋅‖_E = λ‖⋅‖_Łp, where λ= ‖\bf 1‖_E.

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